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Yin Tian

Publications and source records attributed to Yin Tian.

At least 19 recordsLinked to original sources
arXiv2026

Obstructions to smoothing orbicurves and Orbifold Hecke algebras

In this paper, we study obstructions to smoothing nodal orbicurves with orbighosts mapped into cyclic quotient singularities. As an application, we show, under some assumptions, that the orbifold Hecke algebra of a complex global quotient orbifold $[X/G]$ is isomorphic to the degree $0$ cohomology of the $A_\infty$-algebra of endomorphisms of a regular cotangent fiber $T_{[x]}^*[X/G]$ regarded as an object of the bulk-deformed wrapped Fukaya category of the orbifold $T^*[X/G]$ for a compact complex manifold $X$ and finite group $G \subset \operatorname{Aut}(X)$.

math.SG↗
arXiv2026

Higher-dimensional Heegaard Floer homology and spectral networks

Given a closed surface $C$ and a real exact Lagrangian $\Sigma \subset T^*C$ associated to a spectral curve, we construct a homomorphism $\operatorname{BSk}_\kappa(C)\to\operatorname{Mat}(N^{\kappa},\operatorname{BSk}_\kappa(\Sigma))$ from the braid skein algebra of $C$ to the matrix-valued braid skein algebra of $\Sigma$ using Floer theory and in particular higher-dimensional Heegaard Floer homology (HDHF). We sketch a proof that this map coincides with a hybrid Floer-Morse approach which counts HDHF-type holomorphic curves coupled with certain Morse gradient graphs -- called fold\-ed Morse trees -- using a variant of the adiabatic limit theorems of Fukaya-Oh and Ekholm, which compares holomorphic curves and Morse flow trees.

math.SG↗
arXiv2025

Towards a symplectic Khovanov homology for links in fibered $3$-manifolds

The goal of this paper is twofold: (i) define a symplectic Khovanov type homology for a transverse link in a fibered closed $3$-manifold $M$ (with an auxiliary choice of a homotopy class of loops that intersect each fiber once) and (ii) give conjectural combinatorial dga descriptions of surface categories that appear in (i). These dgas are higher-dimensional analogs of the strands algebras in bordered Heegaard Floer homology, due to Lipshitz-Ozsv\'ath-Thurston \cite{LOT}.

math.SG↗
arXiv2025

Homology of Yang-Baxter modules

We study the Yang-Baxter operator for the vector representation $V_m$ of the quantum group $U_q(sl_m)$. We consider the one-term Yang-Baxter homology with coefficients in $V_m$-modules and provide a direct sum decomposition of the one term Yang-Baxter chain complex. The homology is explicitly computed for some specific $V_m$-modules.

math.QA↗
arXiv2025

Morse theory of loop spaces and Hecke algebras

Given a smooth closed $n$-manifold $M$ and a $\kappa$-tuple of basepoints $\boldsymbol{q}\subset M$, we define a Morse-type $A_\infty$-algebra $CM_{-*}(\Omega(M,\boldsymbol{q}))$, called the based multiloop $A_\infty$-algebra, as a graded generalization of the braid skein algebra due to Morton and Samuelson. For example, when $M=T^2$ the braid skein algebra is the Type A double affine Hecke algebra (DAHA). The $A_\infty$-operations couple Morse gradient trees on a based loop space with Chas-Sullivan type string operations. We show that, after a certain "base change", $CM_{-*}(\Omega(M,\boldsymbol{q}))$ is $A_\infty$-equivalent to the wrapped higher-dimensional Heegaard Floer $A_\infty$-algebra of $\kappa$ disjoint cotangent fibers which was studied in the work of Honda, Colin, and Tian. We also compute the based multiloop $A_\infty$-algebra for $M=S^2$, which we can regard as a derived Hecke algebra of the $2$-sphere.

math.SG↗
arXiv2025

CrossFuse: Learning Infrared and Visible Image Fusion by Cross-Sensor Top-K Vision Alignment and Beyond

Infrared and visible image fusion (IVIF) is increasingly applied in critical fields such as video surveillance and autonomous driving systems. Significant progress has been made in deep learning-based fusion methods. However, these models frequently encounter out-of-distribution (OOD) scenes in real-world applications, which severely impact their performance and reliability. Therefore, addressing the challenge of OOD data is crucial for the safe deployment of these models in open-world environments. Unlike existing research, our focus is on the challenges posed by OOD data in real-world applications and on enhancing the robustness and generalization of models. In this paper, we propose an infrared-visible fusion framework based on Multi-View Augmentation. For external data augmentation, Top-k Selective Vision Alignment is employed to mitigate distribution shifts between datasets by performing RGB-wise transformations on visible images. This strategy effectively introduces augmented samples, enhancing the adaptability of the model to complex real-world scenarios. Additionally, for internal data augmentation, self-supervised learning is established using Weak-Aggressive Augmentation. This enables the model to learn more robust and general feature representations during the fusion process, thereby improving robustness and generalization. Extensive experiments demonstrate that the proposed method exhibits superior performance and robustness across various conditions and environments. Our approach significantly enhances the reliability and stability of IVIF tasks in practical applications.

cs.CV↗
arXiv2023

Higher-dimensional Heegaard Floer homology and Hecke algebras

Given a closed oriented surface $Σ$ of genus greater than 0, we construct a map $\mathcal{F}$ from the higher-dimensional Heegaard Floer homology of the cotangent fibers of $T^*Σ$ to the Hecke algebra associated to $Σ$ and show that $\mathcal{F}$ is an isomorphism of algebras. We also establish analogous results for punctured surfaces.

math.SG↗
arXiv2023

String Condensations in 3+1D and Lagrangian Algebras

We present three Lagrangian algebras in the modular 2-category associated to the 3+1D $\mathbb{Z}_2$ topological order and discuss their physical interpretations, connecting algebras with gapped boundary conditions, and interestingly, maps (braided autoequivalences) exchanging algebras with bulk domain walls. A Lagrangian algebra, together with its modules and local modules, encapsulates detailed physical data of strings condensing at a gapped boundary. In particular, the condensed strings can terminate at boundaries in non-trivial ways. This phenomenon has no lower dimensional analogue and corresponds to novel mathematical structures associated to higher algebras. We provide a layered construction and also explicit lattice realizations of these boundaries and illustrate the correspondence between physics and mathematics of these boundary conditions. This is a first detailed study of the mathematics of Lagrangian algebras in modular 2-categories and their corresponding physics, that brings together rich phenomena of string condensations, gapped boundaries and domain walls in 3+1D topological orders.

cond-mat.str-el↗
arXiv2022

An example of higher-dimensional Heegaard Floer homology

We count pseudoholomorphic curves in the higher-dimensional Heegaard Floer homology of disjoint cotangent fibers of a two dimensional disk. We show that the resulting algebra is isomorphic to the Hecke algebra associated to the symmetric group.

math.SG↗
arXiv2021

Contact categories of disks

In the first part of the paper we associate a pre-additive category $\mathcal{C}(Σ)$ to a closed oriented surface $Σ$, called the {\em contact category} and constructed from contact structures on $Σ\times[0,1]$. There are also $\mathcal{C}(Σ,F)$, where $Σ$ is a compact oriented surface with boundary and $F\subset \partialΣ$ is a finite oriented set of points which bounds a submanifold of $\partialΣ$, and universal covers $\widetilde{\mathcal{C}}(Σ)$ and $\widetilde{\mathcal{C}}(Σ,F)$ of $\mathcal{C}(Σ)$ and $\mathcal{C}(Σ,F)$. In the second part of the paper we prove that the universal cover of the contact category of a disk admits an embedding into its "triangulated envelope."

math.SG↗
arXiv2020

CLUE: A Chinese Language Understanding Evaluation Benchmark

The advent of natural language understanding (NLU) benchmarks for English, such as GLUE and SuperGLUE allows new NLU models to be evaluated across a diverse set of tasks. These comprehensive benchmarks have facilitated a broad range of research and applications in natural language processing (NLP). The problem, however, is that most such benchmarks are limited to English, which has made it difficult to replicate many of the successes in English NLU for other languages. To help remedy this issue, we introduce the first large-scale Chinese Language Understanding Evaluation (CLUE) benchmark. CLUE is an open-ended, community-driven project that brings together 9 tasks spanning several well-established single-sentence/sentence-pair classification tasks, as well as machine reading comprehension, all on original Chinese text. To establish results on these tasks, we report scores using an exhaustive set of current state-of-the-art pre-trained Chinese models (9 in total). We also introduce a number of supplementary datasets and additional tools to help facilitate further progress on Chinese NLU. Our benchmark is released at https://www.CLUEbenchmarks.com

cs.CL↗
arXiv2020

Defects in the 3-dimensional toric code model form a braided fusion 2-category

It was well known that there are $e$-particles and $m$-strings in the 3-dimensional (spatial dimension) toric code model, which realizes the 3-dimensional $\mathbb{Z}_2$ topological order. Recent mathematical result, however, shows that there are additional string-like topological defects in the 3-dimensional $\mathbb{Z}_2$ topological order. In this work, we construct all topological defects of codimension 2 and higher, and show that they form a braided fusion 2-category satisfying a braiding non-degeneracy condition.

cond-mat.str-el↗
arXiv2020

Applications of higher-dimensional Heegaard Floer homology to contact topology

The goal of this paper is to set up the general framework of higher-dimensional Heegaard Floer homology, define the contact class, and use it to give an obstruction to the Liouville fillability of a contact manifold and a sufficient condition for the Weinstein conjecture to hold. We discuss several classes of examples including those coming from analyzing a close cousin of symplectic Khovanov homology and the analog of the Plamenevskaya invariant of transverse links.

math.SG↗
arXiv2020

CLUENER2020: Fine-grained Named Entity Recognition Dataset and Benchmark for Chinese

In this paper, we introduce the NER dataset from CLUE organization (CLUENER2020), a well-defined fine-grained dataset for named entity recognition in Chinese. CLUENER2020 contains 10 categories. Apart from common labels like person, organization, and location, it contains more diverse categories. It is more challenging than current other Chinese NER datasets and could better reflect real-world applications. For comparison, we implement several state-of-the-art baselines as sequence labeling tasks and report human performance, as well as its analysis. To facilitate future work on fine-grained NER for Chinese, we release our dataset, baselines, and leader-board.

cs.CL↗
arXiv2020

Towards functor exponentiation

We consider a possible framework to categorify the exponential map exp(-f) given the categorification of a generator f of $\frak{sl}_2$ by Lauda. In this setup the Taylor expansions of exp(-f) and exp(f) turn into complexes built out of categorified divided powers of f. Hom spaces between tensor powers of categorified f are given by diagrammatics combining nilHecke algebra relations with those for a additional "short strand" generator. The proposed framework is only an approximation to categorification of exponentiation, because the functors categorifying exp(f) and exp(-f) are not invertible.

math.QA↗